Abstract

When holograms are used as optical elements two of their properties are of interest: dispersion and aberrations. This paper uses a general hologram analysis computer program based on ray tracing to analyze these properties. Numerical examples are given for both single and multiple element systems where the goal is to reduce the lateral dispersion. A significant reduction in this dispersion is accomplished with the introduction of a plane grating adjacent to the hologram. The problem of reducing the longitudinal dispersion is more complex, and it is studied in the paper by minimizing the variation in focus distance as a function of the reconstruction wavelength for two- and three-element on-axis hologram systems. To optimize the reduction in dispersion and design a system with low aberrations, the hologram ray tracing programs were modified to be driven by an optimization program. These techniques realized a three-element on-axis f/3.84 system with aberrations and dispersions less than 0.32λc and 87 μ, respectively, when operated over a band from 4385 Å to 7060 Å.

Because of the complexity of the equations needed to solve for the variables of interest in the three-element problem, we have used extensively the algebraic manipulation language REDUCE2.12 Such a tool is an invaluable aid in manipulating the long expressions and taking the derivatives, etc.

Because of the complexity of the equations needed to solve for the variables of interest in the three-element problem, we have used extensively the algebraic manipulation language REDUCE2.12 Such a tool is an invaluable aid in manipulating the long expressions and taking the derivatives, etc.